Subgroups — C₇×#60707 #13237923

Order 1792.

1980 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₇×#3180	C₂	1	4	yes	maximal, complemented
3	C₇×#3179	C₂	1	4	yes	maximal, complemented
4	C₇×#3176	C₂	1	2	yes	maximal, complemented
5	C₇×#3175	C₂	1	2	yes	maximal, complemented
6	C₇×#3169	C₂	1	2	yes	maximal, complemented
7	C₇×#3168	C₂	1	2	yes	maximal, complemented
8	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3055	C₂	1	2	yes	maximal, complemented
12	C₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₇×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#555	—	2	2	no	—
24	C₇×#553	—	2	2	no	—
25	C₇×#553	—	2	2	no	—
26	C₇×#551	—	2	4	no	—
27	C₇×#547	—	2	2	no	—
28	C₇×#546	—	2	4	no	—
29	C₇×#544	C₂²	1	2	yes	—
30	C₇×#542	C₂²	1	4	yes	complemented
31	C₇×#540	C₂²	1	4	yes	complemented
32	C₇×#535	C₂²	1	2	yes	—
33	C₇×#532	C₂²	1	4	yes	complemented
34	C₇×#529	C₂²	1	4	yes	complemented
35	C₇×#525	C₂²	1	2	yes	—
36	C₂×C₇×#121	C₂²	1	2	yes	—
37	C₇×#520	C₂²	1	2	yes	—
38	C₇×#518	C₂²	1	2	yes	—
39	C₂×C₇×#117	C₂²	1	1	yes	characteristic
40	C₇×#501	C₂²	1	4	yes	complemented
41	C₇×#500	C₂²	1	2	yes	complemented
42	C₇×#499	C₂²	1	2	yes	complemented
43	C₇×#496	C₂²	1	4	yes	complemented
44	C₇×#495	C₂²	1	2	yes	complemented
45	C₇×#493	C₂²	1	2	yes	complemented
46	C₇×#490	C₂²	1	4	yes	complemented
47	C₇×#489	C₂²	1	4	yes	complemented
48	C₇×#488	C₂²	1	4	yes	complemented
49	C₇×#486	C₂²	1	4	yes	complemented
50	C₇×#469	C₂²	1	4	yes	complemented
51	C₇×#468	C₂²	1	4	yes	complemented
52	C₇×#467	C₂²	1	1	yes	characteristic, complemented
53	C₇×#467	C₂²	1	1	yes	characteristic, complemented
54	C₇×#466	C₂²	1	2	yes	—
55	C₇×#466	C₂²	1	2	yes	—
56	C₇×#466	C₂²	1	2	yes	—
57	C₇×#466	C₂²	1	2	yes	—
58	C₇×#466	C₂²	1	1	yes	characteristic, complemented
59	C₇×#466	C₂²	1	4	yes	complemented
60	C₇×#466	C₂²	1	1	yes	characteristic, complemented
61	C₇×#465	C₂²	1	4	yes	complemented
62	C₇×#465	C₂²	1	2	yes	complemented
63	C₇×#465	C₂²	1	2	yes	complemented
64	C₇×#442	C₂²	1	4	yes	complemented
65	C₇×#442	C₂²	1	4	yes	complemented
66	C₇×#440	C₂²	1	4	yes	complemented
67	C₇×#440	C₂²	1	4	yes	complemented
68	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
69	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
70	C₄×C₇×D₈	C₂²	1	2	yes	complemented
71	C₄×C₇×D₈	C₂²	1	2	yes	complemented
72	C₄×C₇×D₈	C₂²	1	2	yes	complemented
73	C₄×C₇×D₈	C₂²	1	4	yes	complemented
74	C₇×#428	C₂²	1	2	yes	—
75	C₇×#427	C₂²	1	1	yes	characteristic
76	C₂×C₇×#107	C₂²	1	1	yes	characteristic
77	C₇×#418	C₂²	1	2	yes	—
78	C₇×#417	C₂²	1	2	yes	—
79	C₇×#416	C₂²	1	2	yes	—
80	C₂×C₇×#102	C₂²	1	2	yes	—
81	C₇×#405	C₂²	1	1	yes	characteristic
82	C₇×#405	C₂²	1	1	yes	characteristic
83	C₇×#405	C₂²	1	1	yes	characteristic
84	C₇×#405	C₂²	1	1	yes	characteristic
85	C₇×#405	C₂²	1	2	yes	complemented
86	C₇×#405	C₂²	1	2	yes	complemented
87	C₂×C₇×#97	C₂²	1	2	yes	complemented
88	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
89	#60707	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	4	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂²×C₇×D₄	—	2	2	no	—
93	C₂²×C₇×D₄	C₂³	1	2	yes	—
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₇×AGL(1,ℤ/8)	—	2	8	no	—
96	C₇×#135	—	2	4	no	—
97	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₇×D₈	—	2	4	no	—
101	C₂×C₇×D₈	C₂³	1	2	yes	—
102	C₂×C₇×D₈	C₂³	1	2	yes	—
103	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
104	C₂×C₇×D₈	C₂³	1	4	yes	—
105	C₂×C₇×M₁₆	—	2	4	no	—
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	—	2	4	no	—
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₂²×C₇×C₈	C₂³	1	2	yes	—
115	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	—	2	2	no	—
118	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₇×#127	C₂³	1	4	yes	—
120	C₇×#126	—	2	4	no	—
121	C₇×#126	—	2	4	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	C₂³	1	4	yes	—
124	C₇×#124	—	2	4	no	—
125	C₇×#124	—	2	4	no	—
126	C₇×#124	C₂³	1	4	yes	—
127	C₇×#123	—	2	2	no	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×#123	—	2	4	no	—
132	C₇×C₂²⋊Q₈	—	2	4	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₇×#121	—	2	2	no	—
137	C₇×#121	—	2	2	no	—
138	C₇×#121	—	2	4	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	4	no	—
142	C₇×#121	—	2	4	no	—
143	C₇×#121	C₂³	1	4	yes	—
144	C₇×#121	C₂³	1	4	yes	—
145	C₇×#121	C₂³	1	2	yes	—
146	C₇×#121	C₂³	1	2	yes	—
147	C₇×#120	—	2	2	no	—
148	C₇×#120	—	2	4	no	—
149	C₄×C₇×Q₈	C₂³	1	4	yes	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	4	no	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	4	no	—
156	C₄×C₇×D₄	—	2	4	no	—
157	C₄×C₇×D₄	C₂³	1	4	yes	—
158	C₄×C₇×D₄	C₂³	1	4	yes	—
159	C₄×C₇×D₄	C₂³	1	4	yes	—
160	C₇×#117	—	2	2	no	—
161	C₇×#117	—	2	4	no	—
162	C₇×#117	D₄	1	2	yes	—
163	C₇×#117	D₄	1	1	yes	characteristic
164	C₇×#117	D₄	1	1	yes	characteristic
165	C₇×#117	C₂³	1	2	yes	—
166	C₇×#117	C₂³	1	1	yes	characteristic
167	C₇×#117	C₂³	1	1	yes	characteristic
168	C₇×#117	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	—	2	2	no	—
170	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
174	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
175	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
176	C₂×C₄²×C₇	C₂³	1	2	yes	—
177	C₇×#107	C₂³	1	2	yes	—
178	C₇×#107	C₂³	1	2	yes	—
179	C₇×#107	C₂³	1	1	yes	characteristic
180	C₇×#107	C₂³	1	1	yes	characteristic
181	C₇×#107	C₂³	1	4	yes	—
182	C₇×#106	C₂³	1	4	yes	—
183	C₇×#106	C₂³	1	2	yes	—
184	C₇×#103	C₂³	1	2	yes	—
185	C₇×#103	C₂³	1	2	yes	—
186	C₇×#103	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	4	yes	—
188	C₇×#102	C₂³	1	4	yes	—
189	C₇×#102	C₂³	1	4	yes	—
190	C₇×#102	C₂³	1	4	yes	—
191	C₇×#102	C₂³	1	2	yes	—
192	C₇×#102	C₂³	1	2	yes	—
193	C₇×#102	C₂³	1	4	yes	—
194	C₇×#97	C₂³	1	2	yes	—
195	C₇×#97	C₂³	1	2	yes	—
196	C₇×#97	C₂³	1	2	yes	—
197	C₇×#97	C₂³	1	2	yes	—
198	C₄×C₇×C₈	C₂³	1	2	yes	—
199	C₄×C₇×C₈	C₂³	1	2	yes	—
200	C₄×C₇×C₈	C₂³	1	2	yes	—
201	C₄×C₇×C₈	C₂³	1	2	yes	—
202	#3494	C₂×C₇	1	2	yes	complemented
203	#3180	C₂×C₇	1	4	yes	complemented
204	#3179	C₂×C₇	1	4	yes	complemented
205	#3176	C₂×C₇	1	2	yes	complemented
206	#3175	C₂×C₇	1	2	yes	complemented
207	#3169	C₂×C₇	1	2	yes	complemented
208	#3168	C₂×C₇	1	2	yes	complemented
209	#3164	C₂×C₇	1	1	yes	characteristic, complemented
210	#3155	C₂×C₇	1	1	yes	characteristic, complemented
211	#3136	C₂×C₇	1	2	yes	complemented
212	#3055	C₂×C₇	1	2	yes	complemented
213	#3050	C₂×C₇	1	1	yes	characteristic, complemented
214	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
215	#2951	C₂×C₇	1	1	yes	characteristic, complemented
216	#2948	C₂×C₇	1	1	yes	characteristic, complemented
217	#2946	C₂×C₇	1	2	yes	complemented
218	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
219	C₂⁴×C₇	—	2	2	no	—
220	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
221	C₇×#41	—	2	4	no	—
222	C₇×#41	—	2	4	no	—
223	C₇×#41	—	8	8	no	—
224	C₂×C₇×Q₈	—	2	4	no	—
225	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
226	C₂×C₇×D₄	—	2	2	no	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	2	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	2	no	—
232	C₂×C₇×D₄	—	2	4	no	—
233	C₂×C₇×D₄	—	2	4	no	—
234	C₂×C₇×D₄	—	2	4	no	—
235	C₂×C₇×D₄	—	2	4	no	—
236	C₂×C₇×D₄	—	8	4	no	—
237	C₂×C₇×D₄	C₂⁴	1	4	yes	—
238	C₂×C₇×D₄	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇	—	2	2	no	—
240	C₂²×C₄×C₇	—	2	2	no	—
241	C₂²×C₄×C₇	—	2	2	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	—	2	4	no	—
246	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₇×Q₁₆	—	2	2	no	—
255	C₇×SD₁₆	—	2	4	no	—
256	C₇×SD₁₆	—	2	8	no	—
257	C₇×D₈	—	2	4	no	—
258	C₇×D₈	—	2	4	no	—
259	C₇×D₈	—	2	2	no	—
260	C₇×D₈	—	2	8	no	—
261	C₇×M₁₆	—	2	2	no	—
262	C₇×M₁₆	—	2	4	no	—
263	C₇×M₁₆	#41	1	4	yes	complemented
264	C₂×C₇×C₈	—	2	2	no	—
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	2	no	—
267	C₂×C₇×C₈	—	2	2	no	—
268	C₂×C₇×C₈	—	2	2	no	—
269	C₂×C₇×C₈	—	2	4	no	—
270	C₂×C₇×C₈	#41	1	4	yes	complemented
271	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
272	C₂×C₇×C₈	C₂⁴	1	2	yes	—
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	C₂⁴	1	2	yes	—
276	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
277	C₇×C₄⋊C₄	—	2	2	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	2	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
285	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
288	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
289	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₇×C₂²⋊C₄	—	2	2	no	—
294	C₇×C₂²⋊C₄	—	2	2	no	—
295	C₇×C₂²⋊C₄	—	2	2	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
299	C₇×C₂²⋊C₄	—	2	4	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	—	2	4	no	—
302	C₇×C₂²⋊C₄	—	2	2	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
306	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
307	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
308	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
309	C₄²×C₇	—	2	4	no	—
310	C₄²×C₇	—	2	2	no	—
311	C₄²×C₇	C₂×D₄	1	2	yes	—
312	C₄²×C₇	C₂×D₄	1	2	yes	—
313	C₄²×C₇	C₂⁴	1	2	yes	—
314	C₄²×C₇	C₂⁴	1	2	yes	—
315	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
316	C₂×#135	C₂²×C₇	1	1	yes	characteristic
317	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
319	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
320	#555	—	2	2	no	—
321	#553	—	2	2	no	—
322	#553	—	2	2	no	—
323	#551	—	2	4	no	—
324	#547	—	2	2	no	—
325	#546	—	2	4	no	—
326	#544	C₂²×C₇	1	2	yes	—
327	#542	C₂²×C₇	1	4	yes	complemented
328	#540	C₂²×C₇	1	4	yes	complemented
329	#535	C₂²×C₇	1	2	yes	—
330	#532	C₂²×C₇	1	4	yes	complemented
331	#529	C₂²×C₇	1	4	yes	complemented
332	#525	C₂²×C₇	1	2	yes	—
333	C₂×#121	C₂²×C₇	1	2	yes	—
334	#520	C₂²×C₇	1	2	yes	—
335	#518	C₂²×C₇	1	2	yes	—
336	C₂×#117	C₂²×C₇	1	1	yes	characteristic
337	#501	C₂²×C₇	1	4	yes	complemented
338	#500	C₂²×C₇	1	2	yes	complemented
339	#499	C₂²×C₇	1	2	yes	complemented
340	#496	C₂²×C₇	1	4	yes	complemented
341	#495	C₂²×C₇	1	2	yes	complemented
342	#493	C₂²×C₇	1	2	yes	complemented
343	#490	C₂²×C₇	1	4	yes	complemented
344	#489	C₂²×C₇	1	4	yes	complemented
345	#488	C₂²×C₇	1	4	yes	complemented
346	#486	C₂²×C₇	1	4	yes	complemented
347	#469	C₂²×C₇	1	4	yes	complemented
348	#468	C₂²×C₇	1	4	yes	complemented
349	#467	C₂²×C₇	1	1	yes	characteristic, complemented
350	#467	C₂²×C₇	1	1	yes	characteristic, complemented
351	#466	C₂²×C₇	1	2	yes	—
352	#466	C₂²×C₇	1	2	yes	—
353	#466	C₂²×C₇	1	2	yes	—
354	#466	C₂²×C₇	1	2	yes	—
355	#466	C₂²×C₇	1	1	yes	characteristic, complemented
356	#466	C₂²×C₇	1	4	yes	complemented
357	#466	C₂²×C₇	1	1	yes	characteristic, complemented
358	#465	C₂²×C₇	1	4	yes	complemented
359	#465	C₂²×C₇	1	2	yes	complemented
360	#465	C₂²×C₇	1	2	yes	complemented
361	#442	C₂²×C₇	1	4	yes	complemented
362	#442	C₂²×C₇	1	4	yes	complemented
363	#440	C₂²×C₇	1	4	yes	complemented
364	#440	C₂²×C₇	1	4	yes	complemented
365	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
366	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
367	C₄×D₈	C₂²×C₇	1	2	yes	complemented
368	C₄×D₈	C₂²×C₇	1	2	yes	complemented
369	C₄×D₈	C₂²×C₇	1	2	yes	complemented
370	C₄×D₈	C₂²×C₇	1	4	yes	complemented
371	#428	C₂²×C₇	1	2	yes	—
372	#427	C₂²×C₇	1	1	yes	characteristic
373	C₂×#107	C₂²×C₇	1	1	yes	characteristic
374	#418	C₂²×C₇	1	2	yes	—
375	#417	C₂²×C₇	1	2	yes	—
376	#416	C₂²×C₇	1	2	yes	—
377	C₂×#102	C₂²×C₇	1	2	yes	—
378	#405	C₂²×C₇	1	1	yes	characteristic
379	#405	C₂²×C₇	1	1	yes	characteristic
380	#405	C₂²×C₇	1	1	yes	characteristic
381	#405	C₂²×C₇	1	1	yes	characteristic
382	#405	C₂²×C₇	1	2	yes	complemented
383	#405	C₂²×C₇	1	2	yes	complemented
384	C₂×#97	C₂²×C₇	1	2	yes	complemented
385	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
386	C₂³×C₇	—	2	2	no	—
387	C₂³×C₇	—	2	2	no	—
388	C₂³×C₇	—	2	4	no	—
389	C₂³×C₇	—	2	2	no	—
390	C₂³×C₇	—	4	1	no	—
391	C₂³×C₇	—	4	4	no	—
392	C₂³×C₇	—	8	2	no	—
393	C₂³×C₇	—	8	2	no	—
394	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
397	C₇×Q₈	—	2	2	no	—
398	C₇×Q₈	—	2	2	no	—
399	C₇×Q₈	—	8	4	no	—
400	C₇×D₄	—	2	4	no	—
401	C₇×D₄	—	2	2	no	—
402	C₇×D₄	—	2	4	no	—
403	C₇×D₄	—	2	2	no	—
404	C₇×D₄	—	4	4	no	—
405	C₇×D₄	—	4	8	no	—
406	C₇×D₄	—	4	4	no	—
407	C₇×D₄	—	4	4	no	—
408	C₇×D₄	—	8	4	no	—
409	C₇×D₄	—	8	4	no	—
410	C₇×D₄	—	8	2	no	—
411	C₇×D₄	—	8	4	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	1	no	—
417	C₂×C₄×C₇	—	2	1	no	—
418	C₂×C₄×C₇	—	2	1	no	—
419	C₂×C₄×C₇	—	2	1	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	4	no	—
424	C₂×C₄×C₇	—	4	2	no	—
425	C₂×C₄×C₇	—	4	4	no	—
426	C₂×C₄×C₇	—	8	4	no	—
427	C₂×C₄×C₇	—	8	4	no	—
428	C₂×C₄×C₇	—	8	4	no	—
429	C₂×C₄×C₇	—	8	2	no	—
430	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₇	C₂×#41	1	2	yes	—
438	C₂×C₄×C₇	C₂×#41	1	2	yes	—
439	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
440	C₇×C₈	—	2	1	no	—
441	C₇×C₈	—	2	1	no	—
442	C₇×C₈	—	2	2	no	—
443	C₇×C₈	C₂×#41	1	2	yes	—
444	C₇×C₈	C₂×#41	1	2	yes	—
445	C₇×C₈	C₂×#41	1	4	yes	—
446	C₂×#41	—	2	4	no	—
447	C₂×#41	C₂³×C₇	1	2	yes	—
448	C₂²×D₄	—	2	2	no	—
449	C₂²×D₄	C₂³×C₇	1	2	yes	—
450	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
451	AGL(1,ℤ/8)	—	2	8	no	—
452	#135	—	2	4	no	—
453	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
454	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
455	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
456	C₂×D₈	—	2	4	no	—
457	C₂×D₈	C₂³×C₇	1	2	yes	—
458	C₂×D₈	C₂³×C₇	1	2	yes	—
459	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
460	C₂×D₈	C₂³×C₇	1	4	yes	—
461	C₂×M₁₆	—	2	4	no	—
462	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
463	C₂×M₁₆	C₂³×C₇	1	2	yes	—
464	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
465	C₂²×C₈	—	2	4	no	—
466	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₇	1	2	yes	—
472	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
475	#127	C₂³×C₇	1	4	yes	—
476	#126	—	2	4	no	—
477	#126	—	2	4	no	—
478	#125	—	2	2	no	—
479	#125	C₂³×C₇	1	4	yes	—
480	#124	—	2	4	no	—
481	#124	—	2	4	no	—
482	#124	C₂³×C₇	1	4	yes	—
483	#123	—	2	2	no	—
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
491	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	4	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	4	no	—
498	#121	—	2	4	no	—
499	#121	C₂³×C₇	1	4	yes	—
500	#121	C₂³×C₇	1	4	yes	—
501	#121	C₂³×C₇	1	2	yes	—
502	#121	C₂³×C₇	1	2	yes	—
503	#120	—	2	2	no	—
504	#120	—	2	4	no	—
505	C₄×Q₈	C₂³×C₇	1	4	yes	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	C₂³×C₇	1	4	yes	—
514	C₄×D₄	C₂³×C₇	1	4	yes	—
515	C₄×D₄	C₂³×C₇	1	4	yes	—
516	#117	—	2	2	no	—
517	#117	—	2	4	no	—
518	#117	C₇×D₄	1	2	yes	—
519	#117	C₇×D₄	1	1	yes	characteristic
520	#117	C₇×D₄	1	1	yes	characteristic
521	#117	C₂³×C₇	1	2	yes	—
522	#117	C₂³×C₇	1	1	yes	characteristic
523	#117	C₂³×C₇	1	1	yes	characteristic
524	#117	C₂³×C₇	1	2	yes	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
532	C₂×C₄²	C₂³×C₇	1	2	yes	—
533	#107	C₂³×C₇	1	2	yes	—
534	#107	C₂³×C₇	1	2	yes	—
535	#107	C₂³×C₇	1	1	yes	characteristic
536	#107	C₂³×C₇	1	1	yes	characteristic
537	#107	C₂³×C₇	1	4	yes	—
538	#106	C₂³×C₇	1	2	yes	—
539	#106	C₂³×C₇	1	4	yes	—
540	#103	C₂³×C₇	1	2	yes	—
541	#103	C₂³×C₇	1	2	yes	—
542	#103	C₂³×C₇	1	4	yes	—
543	#102	C₂³×C₇	1	4	yes	—
544	#102	C₂³×C₇	1	4	yes	—
545	#102	C₂³×C₇	1	2	yes	—
546	#102	C₂³×C₇	1	2	yes	—
547	#102	C₂³×C₇	1	4	yes	—
548	#102	C₂³×C₇	1	4	yes	—
549	#102	C₂³×C₇	1	4	yes	—
550	#97	C₂³×C₇	1	2	yes	—
551	#97	C₂³×C₇	1	2	yes	—
552	#97	C₂³×C₇	1	2	yes	—
553	#97	C₂³×C₇	1	2	yes	—
554	C₄×C₈	C₂³×C₇	1	2	yes	—
555	C₄×C₈	C₂³×C₇	1	2	yes	—
556	C₄×C₈	C₂³×C₇	1	2	yes	—
557	C₄×C₈	C₂³×C₇	1	2	yes	—
558	C₂²×C₇	—	2	1	no	—
559	C₂²×C₇	—	2	1	no	—
560	C₂²×C₇	—	2	1	no	—
561	C₂²×C₇	—	2	1	no	—
562	C₂²×C₇	—	2	1	no	—
563	C₂²×C₇	—	2	1	no	—
564	C₂²×C₇	—	2	1	no	—
565	C₂²×C₇	—	4	4	no	—
566	C₂²×C₇	—	4	4	no	—
567	C₂²×C₇	—	4	2	no	—
568	C₂²×C₇	—	4	2	no	—
569	C₂²×C₇	—	4	4	no	—
570	C₂²×C₇	—	4	2	no	—
571	C₂²×C₇	—	4	4	no	—
572	C₂²×C₇	—	16	4	no	—
573	C₂²×C₇	#532	1	2	yes	—
574	C₂²×C₇	#576	1	2	yes	—
575	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₇	—	2	2	no	—
577	C₄×C₇	—	2	2	no	—
578	C₄×C₇	—	2	1	no	—
579	C₄×C₇	—	2	1	no	—
580	C₄×C₇	—	2	2	no	—
581	C₄×C₇	—	2	2	no	—
582	C₄×C₇	—	4	2	no	—
583	C₄×C₇	—	4	2	no	—
584	C₄×C₇	—	4	4	no	—
585	C₄×C₇	—	4	2	no	—
586	C₄×C₇	#532	1	2	yes	—
587	C₄×C₇	C₂²×#41	1	1	yes	characteristic
588	C₄×C₇	C₂²×#41	1	1	yes	characteristic
589	C₂⁴	—	2	2	no	—
590	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
591	#41	—	2	4	no	—
592	#41	—	2	4	no	—
593	#41	—	8	8	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	8	4	no	—
607	C₂×D₄	C₂⁴×C₇	1	4	yes	—
608	C₂×D₄	C₂⁴×C₇	1	2	yes	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
617	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
619	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
620	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
624	Q₁₆	—	2	2	no	—
625	SD₁₆	—	2	4	no	—
626	SD₁₆	—	2	8	no	—
627	D₈	—	2	4	no	—
628	D₈	—	2	4	no	—
629	D₈	—	2	2	no	—
630	D₈	—	2	8	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	C₇×#41	1	4	yes	complemented
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	—	2	2	no	—
639	C₂×C₈	—	2	4	no	—
640	C₂×C₈	C₇×#41	1	4	yes	complemented
641	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
642	C₂×C₈	C₂⁴×C₇	1	2	yes	—
643	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
644	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
645	C₂×C₈	C₂⁴×C₇	1	2	yes	—
646	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
655	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
656	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
657	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
659	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
662	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
676	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
677	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
678	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	2	no	—
681	C₄²	C₂×C₇×D₄	1	2	yes	—
682	C₄²	C₂×C₇×D₄	1	2	yes	—
683	C₄²	C₂⁴×C₇	1	2	yes	—
684	C₄²	C₂⁴×C₇	1	2	yes	—
685	C₂×C₇	—	2	2	no	—
686	C₂×C₇	—	2	2	no	—
687	C₂×C₇	—	4	1	no	—
688	C₂×C₇	—	8	2	no	—
689	C₂×C₇	—	8	4	no	—
690	C₂×C₇	C₂×#532	1	1	yes	characteristic
691	C₂×C₇	C₂×#576	1	1	yes	characteristic
692	C₂×C₇	#3584	1	1	yes	characteristic
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	8	2	no	—
700	C₂³	—	8	2	no	—
701	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
702	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
703	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	8	4	no	—
707	D₄	—	2	4	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	4	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	4	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	2	no	—
718	D₄	—	8	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
738	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
739	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
740	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
741	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
742	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
743	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
744	C₂×C₄	C₂×C₇×#41	1	2	yes	—
745	C₂×C₄	C₂×C₇×#41	1	2	yes	—
746	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
747	C₈	—	2	1	no	—
748	C₈	—	2	1	no	—
749	C₈	—	2	2	no	—
750	C₈	C₂×C₇×#41	1	2	yes	—
751	C₈	C₂×C₇×#41	1	2	yes	—
752	C₈	C₂×C₇×#41	1	4	yes	—
753	C₇	#60707	1	1	yes	characteristic, direct product factor, Sylow
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	16	4	no	—
769	C₂²	C₇×#532	1	2	yes	—
770	C₂²	C₇×#576	1	2	yes	—
771	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	4	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	C₇×#532	1	2	yes	—
783	C₄	C₂²×C₇×#41	1	1	yes	characteristic
784	C₄	C₂²×C₇×#41	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	2	no	—
787	C₂	—	4	1	no	—
788	C₂	—	8	4	no	—
789	C₂	—	8	2	no	—
790	C₂	C₂×C₇×#532	1	1	yes	characteristic
791	C₂	C₂×C₇×#576	1	1	yes	characteristic
792	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₇×#3180	C₂	semidirect
3. C₇×#3179	C₂	semidirect
4. C₇×#3176	C₂	semidirect
5. C₇×#3175	C₂	semidirect
6. C₇×#3169	C₂	semidirect
7. C₇×#3168	C₂	semidirect
8. C₇×#3164	C₂	semidirect
9. C₇×#3155	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3055	C₂	semidirect
12. C₇×#3050	C₂	semidirect
13. C₂×C₇×#466	C₂	semidirect
14. C₇×#2951	C₂	semidirect
15. C₇×#2948	C₂	semidirect
16. C₇×#2946	C₂	semidirect
17. C₂×C₇×#405	C₂	semidirect
30. C₇×#542	C₂²	semidirect
31. C₇×#540	C₂²	semidirect
33. C₇×#532	C₂²	semidirect
34. C₇×#529	C₂²	semidirect
40. C₇×#501	C₂²	semidirect
41. C₇×#500	C₂²	semidirect
42. C₇×#499	C₂²	semidirect
43. C₇×#496	C₂²	semidirect
44. C₇×#495	C₂²	semidirect
45. C₇×#493	C₂²	semidirect
46. C₇×#490	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#488	C₂²	semidirect
49. C₇×#486	C₂²	semidirect
50. C₇×#469	C₂²	semidirect
51. C₇×#468	C₂²	semidirect
52. C₇×#467	C₂²	semidirect
53. C₇×#467	C₂²	semidirect
58. C₇×#466	C₂²	semidirect
59. C₇×#466	C₂²	semidirect
60. C₇×#466	C₂²	semidirect
61. C₇×#465	C₂²	semidirect
62. C₇×#465	C₂²	semidirect
63. C₇×#465	C₂²	semidirect
64. C₇×#442	C₂²	semidirect
65. C₇×#442	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₇×#440	C₂²	semidirect
68. C₄×C₇×Q₁₆	C₂²	semidirect
69. C₄×C₇×SD₁₆	C₂²	semidirect
70. C₄×C₇×D₈	C₂²	semidirect
71. C₄×C₇×D₈	C₂²	semidirect
72. C₄×C₇×D₈	C₂²	semidirect
73. C₄×C₇×D₈	C₂²	semidirect
85. C₇×#405	C₂²	semidirect
86. C₇×#405	C₂²	semidirect
87. C₂×C₇×#97	C₂²	semidirect
88. C₂×C₄×C₇×C₈	C₂²	semidirect
89. #60707	C₇	direct (N × H)
202. #3494	C₂×C₇	semidirect
203. #3180	C₂×C₇	semidirect
204. #3179	C₂×C₇	semidirect
205. #3176	C₂×C₇	semidirect
206. #3175	C₂×C₇	semidirect
207. #3169	C₂×C₇	semidirect
208. #3168	C₂×C₇	semidirect
209. #3164	C₂×C₇	semidirect
210. #3155	C₂×C₇	semidirect
211. #3136	C₂×C₇	semidirect
212. #3055	C₂×C₇	semidirect
213. #3050	C₂×C₇	semidirect
214. C₂×#466	C₂×C₇	semidirect
215. #2951	C₂×C₇	semidirect
216. #2948	C₂×C₇	semidirect
217. #2946	C₂×C₇	semidirect
218. C₂×#405	C₂×C₇	semidirect
263. C₇×M₁₆	#41	semidirect
270. C₂×C₇×C₈	#41	semidirect
327. #542	C₂²×C₇	semidirect
328. #540	C₂²×C₇	semidirect
330. #532	C₂²×C₇	semidirect
331. #529	C₂²×C₇	semidirect
337. #501	C₂²×C₇	semidirect
338. #500	C₂²×C₇	semidirect
339. #499	C₂²×C₇	semidirect
340. #496	C₂²×C₇	semidirect
341. #495	C₂²×C₇	semidirect
342. #493	C₂²×C₇	semidirect
343. #490	C₂²×C₇	semidirect
344. #489	C₂²×C₇	semidirect
345. #488	C₂²×C₇	semidirect
346. #486	C₂²×C₇	semidirect
347. #469	C₂²×C₇	semidirect
348. #468	C₂²×C₇	semidirect
349. #467	C₂²×C₇	semidirect
350. #467	C₂²×C₇	semidirect
355. #466	C₂²×C₇	semidirect
356. #466	C₂²×C₇	semidirect
357. #466	C₂²×C₇	semidirect
358. #465	C₂²×C₇	semidirect
359. #465	C₂²×C₇	semidirect
360. #465	C₂²×C₇	semidirect
361. #442	C₂²×C₇	semidirect
362. #442	C₂²×C₇	semidirect
363. #440	C₂²×C₇	semidirect
364. #440	C₂²×C₇	semidirect
365. C₄×Q₁₆	C₂²×C₇	semidirect
366. C₄×SD₁₆	C₂²×C₇	semidirect
367. C₄×D₈	C₂²×C₇	semidirect
368. C₄×D₈	C₂²×C₇	semidirect
369. C₄×D₈	C₂²×C₇	semidirect
370. C₄×D₈	C₂²×C₇	semidirect
382. #405	C₂²×C₇	semidirect
383. #405	C₂²×C₇	semidirect
384. C₂×#97	C₂²×C₇	semidirect
385. C₂×C₄×C₈	C₂²×C₇	semidirect
633. M₁₆	C₇×#41	semidirect
640. C₂×C₈	C₇×#41	semidirect
753. C₇	#60707	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3494	2
C₇×#3180	2
C₇×#3179	2
C₇×#3176	2
C₇×#3175	2
C₇×#3169	2
C₇×#3168	2
C₇×#3164	2
C₇×#3155	2
C₇×#3136	2
C₇×#3055	2
C₇×#3050	2
C₂×C₇×#466	2
C₇×#2951	2
C₇×#2948	2
C₇×#2946	2
C₂×C₇×#405	2
#60707	7

Subgroups — C7×#60707 #13237923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60707 #13237923